Problem: Simplify. Rewrite the expression in the form $4^n$. $\left(4^2\right)^{4}=$
$\begin{aligned} \left(4^2\right)^{4}&=4^{2\cdot 4} \\\\ &=4^8 \end{aligned}$ This follows from the general rule $\left(x^m\right)^{n}=x^{m\cdot n}$. We can also see this is correct by expanding the powers. $\begin{aligned} \left(4^2\right)^{4}&=\underbrace{4^2\cdot 4^2\cdot 4^2\cdot 4^2}_\text{4 times} \\\\\\ &=\underbrace{ \underbrace{4\cdot 4}_\text{2 times} \cdot \underbrace{4\cdot 4}_\text{2 times} \cdot \underbrace{4\cdot 4}_\text{2 times} \cdot \underbrace{4\cdot 4}_\text{2 times}} _\text{4 times} \\\\ &=4^8 \end{aligned}$ In conclusion, $\left(4^2\right)^{4}=4^8$.